I.-C. Leu et al. Materials Chemistry and Physics 56(1998)256-261 iation may alter the contact area of a liquid droplet on the substrate, which in turn gives rise to the growth of whiskers with corresponding diameter variation. However, the depend ence of the diameter of liquid droplets on their wetting behav- ior during whisker growth has not been discussed in detail yet. In the following, a simple estimation as well as its exper imental verification for assessing the geometricalrelationship between the diameter of a liquid droplet lying on the subst and that on the top of a whisker will be carried out. In the 6=65 meanwhile, the relationships between the diameter of a liquid droplet(2ra)on a whisker tip and wh e2=30 the root(2rc)and at the steady-state growth stage(2rw)will also be considered. The reported conclusion that the whisker (b) r"r, sin62 Fig. 2. Schematic cross sections taken through the center for (a)a liquid diameter is determined by the diameter of liquid droplets [10] will then be critically evaluated. Fig. 2(a)and(b) larger volume of liquid A will result in more area being cap from now on in this study lying on the substrate and a overed(d,>d, ) Therefore, the wetting behavior of a liquid VLS-grown whisker with a spherical liquid droplet on its tip, droplet on a solid substrate balanced by its volume can infu- respectively. The variation of droplet shape is due to changes ence the contact area of the VLS liquid droplet, which in turn in the contact angle of the liquid droplet at different stages of affects the size of the whisker precipitated. This wetting growth. According to a geometrical estimation using the behavior can be used to explain the reported results that the appropriate parameters shown in Fig. 2, the volumes of the diameter of liquid droplets is generally found to be larger cap and the droplet can be expressed as follows [6, 13, 14] or at least equal to the diameter of whiskers for various kinds of whiskers prepared by the addition of liquid- Veap3sin 6, /(2+cos 01)(1-cos 01)2 forming agents with varying wetting characteristics. Under the condition where liquid droplets of the same volume are considered, the contact area of the liquid droplet can now be Varoplet 3T7G-3ad(2+cos B2)(1-cos 62) determined by the wetting behavior of the liquid-solid pair concerned. Unfortunately, the wetting characteristics of liq- where Vean is the volume of the liquid cap on graphite, Vd tip, re the radius of the circular contact area of the liquid cap tion of processing parameters. on the graphite substrate as well as the radius of the whisker According to the evolution of whisker morphology, the root, ra the radius of the liquid droplet on the Sic whisker nucleation and growth process of whiskers can be divided tip, B, the contact angle of the liquid cap on the graphite into three stages. These are the nucleation stage, the transient substrate, o the contact angie of the liquid droplet on the Sic growth stage and the steady-state growth stage, which are whisker and B2 is the complementary angle to as shown characterized by an incubation period, growth of whiskers with variable diameter and growth of whiskers with constant Fig 3 shows SEM micrographs for the droplet at different diameter, respectively [15]. As described above, variation in stages of whisker growth. The measured magnitudes of 8, the wetting characteristics as exhibited by contact-angle var- and c are about 65 and 150, respectively. An angle B2 of 30 25k3;B 当Hm日2日42 ig. 3. SEM micrographs of the droplet at different growth stages for(a) a liquid cap on the substrate and (b)a whisker at the steady-state growth stage258 L-C. Leu et al. ~Materials Chemistry and Physics 56 (t998) 256-26t substrate NN~ r~ sinO~ Ol = 65° ,,,o =150' 02=30 ° (a) (b) r, =r~.sin02 Fig. 2. Schematic cross sections taken through the center for (a) a Iiquid cap on the substrate and (b) a liquid droplet on the whisker tip. larger volume of liquid A will result in more area being covered (dl > d3). Therefore, the wetting behavior of a liquid droplet on a solid substrate balanced by its volume can influ￾ence the contact area of the VLS liquid droplet, which in turn affects the size of the whisker precipitated. This wetting behavior can be used to explain the reported results that the diameter of liquid droplets is generally found to be larger [6,t3,14] or at least equal to the diameter of whiskers for various kinds of whiskers prepared by the addition of liquid￾forming agents with varying wetting characteristics. Under the condition where liquid droplets of the same volume are considered, the contact area of the liquid droplet can now be determined by the wetting behavior of the liquid-solid pair concerned. Unfortunately, the wetting characteristics of liq￾uid droplets on solid substrates are highly sensitive to the growth ambient and are thus easily influenced by the fluctu￾ation of processing parameters. According to the evolution of whisker morphology, the nucleation and growth process of whiskers can be divided into three stages. These are the nucleation stage, the transient growth stage and the steady-state growth stage, which are characterized by an incubation period, growth of whiskers with variable diameter and growth of whiskers with constant diameter, respectively [ 15 ]. As described above, variation in the wetting characteristics as exhibited by contact-angle vat￾iation may alter the contact area of a liquid droplet on the substrate, which in turn gives rise to the growth of whiskers with corresponding diameter variation. However, the depend￾ence of the diameter of liquid droplets on their wetting behav￾ior during whisker growth has not been discussed in detail yet. In the following, a simple estimation as well as its exper￾imental verification for assessing the geometrical relationship between the diameter of a liquid droplet lying on the substrate and that on the top of a whisker will be carried out. In the meanwhile, the relationships between the diameter of a liquid droplet (2ra) on a whisker tip and whisker diameters both at the root (2ro) and at the steady-state growth stage (2rw) will also be considered. The reported conclusion that the whisker diameter is determined by the diameter of liquid droplets [ 10] will then be critically evaluated. Fig. 2(a) and (b) depicts a spherical-cap-shaped liquid droplet (called a liquid cap from now on in this study) lying on the substrate and a VLS-grown whisker with a spherical liquid droplet on its tip, respectively. The variation of droplet shape is due to changes in the contact angle of the liquid droplet at different stages of growth. According to a geometrical estimation using the appropriate parameters shown in Fig. 2, the volumes of the cap and the droplet can be expressed as follows: 1[ ro ,~3 V~p = g r~ si---~l ) (2+cos 0,)(1-cos 0,) z (1) 4 1 3 Vdrop,e, = grrr2- ~rra (2+cos 02)(1--cos 02) 2 (2) where Vcap is the volume of the liquid cap on graphite, Vdropl~t the volume of the spherical liquid droplet on the SiC whisker tip, re the radius of the circular contact area of the liquid cap on the graphite substrate as well as the radius of the whisker root, ra the radius of the liquid droplet on the SiC whisker tip, O, the contact angle of the liquid cap on the graphite substrate, q~ the contact angle of the liquid droplet on the SiC whisker and 02 is the complementary angle to q~ as shown in Fig. 2. Fig. 3 shows SEM micrographs for the droplet at different stages of whisker growth. The measured magnitudes of 0t and q~ are about 65 and 150 °, respectively. An angle 02 of 30 ° Fig. 3. SEM micrographs of the droplet at different growth stages for (a) a liquid cap on the substrate and (b) a whisker at the steady-state growth stage